TheAyProblem forp−H3

Abstract

We present evidence that numerically accurate quantum calculations employing modern internucleon forces do not reproduce the proton analyzing power, A(y), for p- 3He elastic scattering at low energies. These calculations underpredict new measured analyzing powers by approximately 30% at E(c.m.) = 1.20 MeV and by 40% at E(c.m.) = 1.69 MeV, an effect analogous to a well-known problem in p-d and n-d scattering. The calculations are performed using the complex Kohn variational principle and the (correlated) hyperspherical harmonics technique with full treatment of the Coulomb force. The inclusion of the three-nucleon interaction does not improve the agreement with the experimental data.

Proton-He3elastic scattering at low energies

“…The zero-energy quantities for this case are more difficult to evaluate. Approximate values of the triplet and singlet scattering lengths have been determined from effective range extrapolations [21] to zero energy of data taken mostly above 1 MeV, and therefore suffer large uncertainties [10]. This problem has been reconsidered recently by George and Knutson [15]; this new phase-shift analysis (PSA) gave two possible sets of scattering-length values, both of which are at variance with the theoretical estimates (see the discussion in Ref.…”

“…For example, the proton analyzing power A y in p-3 He elastic scattering is underestimated by theory at the peak of the angular distribution by about 40% [10]. Other disagreements are discussed in Refs.…”

“…The same increases in computational power, however, have opened the possibility for accurate calculations of the 4N observables using realistic models for nucleon-nucleon (N N ) and three-nucleon (3N ) forces. These calculations have been performed mainly by means of the Faddeev-Yakubovsky (FY) approach [6,7,8] and the Kohn variational principle [9,10,11,12,13]. In spite of this progress, some disagreements still exist between theoretical groups, as for example, in the calculation of the n-3 H total cross section in the peak region (around E c.m.…”

Four-nucleon scattering: a new numerical approach

“…These problems persist even when the Coulomb interaction is added [1,2,3] and seem to be insensitive to the choice of realistic 2N + 3N force model. As it has already been highlighted in the past [4,5,6], the four-nucleon scattering problem reveals further discrepancies between theory and experiment that need clarification in terms of improved calculations using modern force models and efficient numerical algorithms that allow for a numerically converged solution of the Alt, Grassberger and Sandhas (AGS) equation [7] for the transition operators.…”

Reactions in the four-nucleon system above breakup threshold

“…However, their numerical solution using realistic force models only became possible many years later. In the last decade accurate numerical calculations for low-energy nucleon-trinucleon elastic scattering have been performed using both coordinate-space and momentum-space rigorous approaches, namely, the hyperspherical harmonics (HH) expansion method [4,5], the Faddeev-Yakubovsky (FY) equations [1] for the wave function components [6], and the Alt, Grassberger and Sandhas (AGS) equations [3] for transition operators [7,8]. The reliability of all these methods was confirmed in a benchmark calculation [9] for neutron-3 H (n-3 H) and proton-3 He (p-3 He) elastic scattering observables.…”